Many substances, especially those found in biological fluids, can be made to react with appropriate reagent(s) in stoichiometric chemical reactions generating products which are optically active. Many methods have been developed for quantitative determination of such substances as glucose, urea, total carbon dioxide, chloride, and the like taking advantage of such reactions. Typically, one or more of the products of such reactions would create a change in the light transmission through the solution, and spectrophotometers have been used to determine the variation in transmitted light, and therefrom calculating, from known molar absorption coefficients, the concentration of the substance of interest. Alternatively, the products of the reaction may be reacted with a color forming agent and a colorimetric analysis may be made to provide a quantitative indication of the substance in the original soluion. Or instead, the reaction may produce heat or the product of the reaction may conduct electrical current. In these latter cases, calorimetric or conductimetric methods have been used for the determination of the concentration of one or several of the chemical substances participating in the chemical reaction.
Many reactions, on the other hand, give rise to the production of an acid or a base, whose ionization leads, in certain pH ranges to the liberation or the uptake of hydrogen ions.
For example, glucose in solution can be transformed by the addition of the enzyme glucose oxidase (GOD), into gluconic acid, according to the reaction ##EQU1##
Since reaction (1) can be made to occur in a medium having a known pH value, the determination of .DELTA.[H.sup.+ ], i.e., of the number of hydrogen ions liberated in the reaction, can be used to determine stoichiometrically the concentration of glucose, or, in principle, of any other substance producing or absorbing hydrogen ions in solution. However, in order to carry out such reactions it is necessary that the pH value of the medium does not change below or above certain limits. This is assured by the use of buffer solutions, which are a group of substances able to engage themselves into ionization reactions. The theoretical principles underlying such concepts are well known and are exhaustively treated in any textbook relating to the physical chemistry of electrolytic solutions.
In order to determine .DELTA.[H.sup.+ ] produced in reaction (1), use can be made of the equation EQU dbH=.beta..times.d[H.sup.+ ] (2)
where dpH and d[H.sup.+ ] are infinitesimal changes in the pH value of the solution caused by an infinitesimal amount of hydrogen ions, and .beta. is the so called "buffer value" of the solution. .beta., in turn, is a function of the concentration of buffers in solutions, of their respective ionization constants, and of the pH of the solution, according to the equation ##EQU2## where the number of buffer species present in solution, whose individual concentration is C.sub.(i), varies between l and n. .alpha..sub.i is the fractional ionization of each species, given by the formula EQU .alpha..sub.i =1/(1+10.sup.pK(i)-pH) (4)
wherein pK equals, for each species, -log K.sub.(i), where K.sub.(i) is the ionization constant of the buffer component i.
Integration of equation (2) over a definite pH range gives equation (5): EQU .DELTA.[H.sup.+ ]=.beta.(pH(l)-pH(o))=.beta..DELTA.pH (5)
In this integration, it is assumed that the titration curve of the solution is a straight line over the pH range investigated. .DELTA.[H.sup.+ ] is the number of hydrogen ions, in moles per liter, which are required to change the pH value of the solution between pH(o) and pH(l). Typical values of .beta. for biological solutions at pH=7.4 are .beta.=7.5.times.10.sup.-3 moles per liter per pH unit (plasma or serum) and .beta.=30.times.10.sup.-3 moles per liter per pH unit (whole blood). Thus the amount of hydrogen ions required to change the pH of plasma or blood, by one pH unit is respectively 7.5.times.10.sup.-3 moles/liter for plasma and 30.times.10.sup.-3 moles/liter for blood.
According to the present state of the art, pH measurements on whole blood or plasma by a glass and reference electrode combination, using commercially available electrometers, can achieve resolution no better than .+-.0.001 pH units, and even then under only ideal laboratory conditions. Application of equation (5) immediately shows that, for this case, it is possible according to the present state of the art, to estimate, by simple pH measurements, hydrogen ion uptake or release with a sensitivity of 7.5.times.10.sup.-3 .times.10.sup.-3 =7.5.times.10.sup.-6 moles/liter in undiluted plasma and of 3.times.10.sup.-5 moles/liter in whole blood. Since the concentration of many metabolites of clinical interest in biological fluids lies in the concentration range of 5 to 0.1.times.10.sup.-3 moles/liter, the considerations reported above indicate, at least in principle, the usefullness of applying electrochemical methods based on pH measurements to the estimation of the concentration of many chemical species of physiological interest, such as urea, glucose, uric acid, etc. It should be added that the estimation of the amount of hydrogen ions released or absorbed in a chemical reaction by pH electrode measurements can be obtained irrespectively of the optical quality of the sample, which severely limits the application of spectrophotometric methods to the study of whole blood or other turbid solutions.
A close analysis of the analytical instrumentation so far commercially produced shows, however, that no instruments of practical use suitable for the determination of substrates or enzymes in solution using the pH measurement approach have yet been made available. This is not surprising since a more detailed analysis of the problem does indeed reveal several practical difficulties. These can be summarized as follows.
(a) The buffer power of samples such as blood or plasma obtained from different individuals is not constant. Thus the estimation of .DELTA.[H.sup.+ ] produced in a chemical reaction from the measurement of pH requires an accurate estimate of the buffer power of the sample or, alternatively, that the buffer power of the sample be made negligible compared with the buffer power of the medium where the reaction is made to occur.
(b) Most commercial analyzers based, for instance, on light absorption measurements require a few microliters only of sample solution, which is conveniently diluted into a more sizable (0.5 to 3.0 ml) volume of reagent solution. Application of a similar dilution step would also be necessary prior to pH measurement, but unfortunately would proportionally decrease the concentration of the substance to be determined and the size of the .DELTA.pH measurement. Thus dilution of a blood containing 5.0.times.10.sup.-3 moles per liter glucose in a 1:100 ratio would reduce the concentration of the glucose to 5.times.10.sup.-5 moles/liter. Addition of glucose oxidase as per reaction (1) would then release a maximum amount of 5.times.10.sup.-5 moles/liter of hydrogen ions. In a medium with a buffer equal to 5.times.10.sup.-3 moles/liter per pH unit, which is a minimum figure if accurate pH measurements are to be made, this would cause of change in pH of 5.times.10.sup.-5 /5.times.10.sup.-3 =0.01 pH units, far too small be to measured accurately with an error of a few percent by available techniques.
(c) pH measurements to .+-.0.0001 pH units required to obtain the concentration of glucose would also necessitate a high stability in the temperature of the measuring electrodes and of the solutions, adding further complications to the pH measurement approach.
More recently, an electrometric method for the measurement of small pH changes down to .+-.5.times.10.sup.-5 pH units, in biological solutions, has been reported by Luzzana et al, Anal. Biochem., 43:556-563, 1971. The technique is based on the use of two glass electrodes, one of which is used as a reference electrode. This approach has the advantage of eliminating (a) spurious pH drifts due to side reactions frequently found in biological samples, and (b) variations in junction potentials which are known to occur, in the traditional approach of pH measurement using a pH glass electrode and a calomel reference electrode, at the junction between saturated KCl solutions of the reference electrode and the solution under measurement.
Although the principle outlined by Luzzana et al has found several interesting applications in the specialized field of biochemistry, no practical commercial application of this principle has yet been described. This again was to be expected since all described applications of this technique have been, before the disclosure of the present invention, far from simple enough to be used by nonspecialized personnel. The main difficulties in the prior art can be traced to the following points: (a) the two glass electrodes in the apparatus described by Luzzana et al are located in separate compartments which have to be accurately thermostatted to obtain the required stability in reading; (b) the renewal of fresh test solutions in contact with the two electrodes could not be accomplished automatically and required at least a few minutes of manual operations; (c) the volume of the reactions required for each single measurement was at least 10 ml, thus preventing the use of microsamples of the solution under tests; (d) the junction solution between the two test solutions could not be renewed automatically; and (e) all calculations required to obtain the concentration of a given substance under test from the measured values of pH had to be obtained by hand calculation. The present invention overcomes such difficulties, making possible the development of an entirely new apparatus which can automatically estimate the concentration of many substances of interest in the field of clinical chemistry, biochemistry and analytical chemistry.
According to the present invention, the pH of (a) a solution containing the substance of interest and (b) of the same solution to which a small amount of a specific reagent such as, for example, an enzyme, has been added, is measured by two pH electrodes. The difference in pH between the two solutions (.DELTA.pH), when corrected for small blank effects due to the addition of reagents, is free from aspecific drifts in pH and is related only to the effect of the specific reaction. Since under appropriate conditions .DELTA.pH is a function of the amount of .DELTA.[H.sup.+ ], i.e. of the hydrogen ions produced or absorbed by the reaction, .DELTA.[H.sup.+ ] can be obtained by calculation from .DELTA.pH, whence, from the stoichiometry of the reaction, the concentration of the substance of interest can be determined.
The reagent solution should include a buffer capable of maintaining the reaction medium within a range in which the titration curve for the specific reaction is substantially linear. Ordinarily this would be a range of no greater than 1 pH unit and more preferably no greater than 0.5 pH unit, and most preferably within a range of no greater than 0.1 pH unit.
All substances participating in a chemical reaction resulting in an uptake or release of hydrogen ions can be determined by this method and apparatus, which may then find application in many fields such as in clinico-chemistry, in the food and beverage industry, in analytical chemistry, etc. Typical substances which may be determined by this technique are glucose, urea, total carbon dioxide, chloride, and generally all metabolites which are connected through the adenosine triphosphate/adenosine diphosphate (ATP/ADP) system and the diphosphopyridine nucleotide and its reduced form (NAD.sup.+ /NADH) system to a change in hydrogen ion concentration in solution.
The basic components of the apparatus described herein are:
(a) a cuvette which is automatically filled with a known amount of a solution of the substance(s) to be determined;
(b) a cell provided with two glass capillary microelectrodes for the measurement of pH;
(c) means for filling the cuvette with a known amount of solution, for adding a suitable amount of additional reactant(s) and for filling the two pH electrodes with the solution contained in the cuvette before and after the addition of the reactant(s);
(d) a differential analog amplifier, an analog-to-digital converter, a microprocessor run by appropriate instructions, a digital readout and various electrical and electronic accessory circuits to produce a digital indication of the concentration of the substance under test.
Thus the present invention provides a number of advantages over conventional methods of analysis such as those employing colorimetric methods. For example, the present invention employs very stable and durable sensors, i.e., the two pH electrodes, and does not depend on optical measurements. Thus the method and apparatus may be used for the determination of chemical substances in turbid solutions or in solutions of high optical absorbancy such as diluted plasma, blood, syrups, beverages, or products of the food or cosmetic industry. The invention is highly sensitive since a change of .+-.0.0001 pH units can be easily measured, leading to the determination of substances present in solution at very low concentrations (10.sup.-5 moles/liter or less).
The invention also used a relatively small number of proven electronic and mechanical components, and under the control of the microprocessor program, it automatically performs all of the analytical steps required for the analysis and gives final results of the concentration of the substance of interest in a digital form. Further, analysis by the invention herein is reproducible to about 2%, and uses microvolumes of the solution to be analysed (10 microliters or less). The complete analysis may be accomplished in about 40 seconds to provide the final results from the beginning of the analysis.
The method of the invention involves use of the formula: EQU [substance]=FCAL.times.(.DELTA.pH.sub.c -.DELTA.pH.sub.b -.DELTA.pH.sub.o) (6)
wherein [substance] represents the concentration of the substance in question, "FCAL" represents a calibration factor which is a combination of .beta. and a dilution factor, .DELTA.pH.sub.c represents the .DELTA.pH value of the solution after reaction, .DELTA.pH.sub.b represents the .DELTA.pH.sub.b value of the solution of the reagents, but without the sample, and .DELTA.pH.sub.o represents the .DELTA.pH value indicative of the level of noise and drift of the machine components.